Nineteen people, including 12 Pakistani nationals, were arrested in Saudi Arabia after suicide attacks on Monday, including one near Islam's second-holiest site in the city of Medina, the kingdom's Interior Ministry said on Thursday.

A spokesperson said in a statement that authorities had also identified the suicide attackers who struck in Medina, at a Shia mosque in Qatif and in western Jeddah, the economic capital, not far from the US consulate.

One of the suicide bombers responsible for killing four police officers in Medina was identified by the ministry as Naer Muslim Hamad, a 26-year-old Saudi.

Hamad had a history of drug abuse, the ministry said.

Four people were killed in the Medina explosion near the Prophet's Mosque, which came as Muslims prepared for this week's Eid al-Fitr festival marking the end of the holy fasting month of Ramadan.

Body parts of three people were found after another suicide bombing in the mostly Shia Gulf city of Qatif, the ministry said earlier.

It identified the three suspected of carrying out the suicide attacks in Qatif as Ibrahim al-Omar 20, Abdulrahman al-Omar, 23, and 20-year-old Abdulkarim al-Husni.

None had Saudi IDs, according to the ministry, and their nationalities were still unclear.

Two police officers were wounded in the Jeddah attack.

The US embassy in Riyadh reported no casualties among consulate staff from the attack, which coincided with its 4 July Independence Day holiday.

Saudi Crown Prince Mohammed bin Nayef, the interior minister, while visiting wounded policemen in Jeddah said the attacks would "only increase our solidarity and make us stronger".

No group has yet claimed responsibility for Monday's attacks.

However, a series of bombings and shootings claimed by the Islamic State (IS) group in Saudi Arabia since late 2014 has targeted Shia Muslims as well as security forces, killing dozens.

Most attacks have taken place in Eastern Province, home to the majority of the country's Shia minority.

IS leader Abu Bakr al-Baghdadi has called for attacks against Saudi Arabia, which is taking part in the US-led coalition bombing the group in Syria and Iraq.